A variable step size bias-compensated affine projection algorithm with noisy inputs

Abstract

This paper presents an innovative adaptive filtering algorithm that combines bias compensation and variable step size techniques to improve performance in the presence of input noise. In the affine projection algorithm (APA), deriving the bias compensation vector has traditionally been challenging due to the relationship between iterative variables and the input matrix. To address this, we introduce a novel input noise projection vector that enables the accurate derivation of the bias compensation vector, effectively mitigating bias within the APA framework. Additionally, an MSD analysis is applied to the APA update equation, incorporating the bias compensation vector to derive an optimal step size. The proposed algorithm’s performance is verified through simulations, showing improved convergence and lower steady-state error, emphasizing its capability in overcoming the shortcomings of traditional algorithms.